A search for a heavy electron of the type considered by Low and Blackmon has been made by studying the inelastic scattering of 5 BeV electrons from hydrogen. The search was made over a range of values of the mass of the heavy electron from 100 t0 1300 MeV. No evidence for such a particle was observed. Upper limits on the production cross sections were determined and employed to deducelimits on the values of the electron-photon-heavy electron coupling constant in Low and Blackmon=s theory.